A modern inertial navigation unit generally comprises inertial sensors such as gyros and accelerometers arranged on axes of a measurement axis system associated with a support platform for the inertial unit. The gyros measure angular rotations of the measurement axis system relative to a geographical frame of reference and they supply the attitude of the vehicle in the geographical frame of reference. The accelerometers measure accelerations that are projected onto the geographical frame of reference and then integrated a first time in order to provide speed, and then a second time in order to provide position. The accuracy of an inertial navigation unit depends directly on the errors of the inertial sensors (gyros and accelerometers), and more precisely on the projection of those errors onto the local geographical frame of reference; and when performing long-term inertial navigation, the position errors depend mainly on the accuracy of the gyros. The accuracy of the gyros is affected by drift errors (shifting of the measurement origin, such that a magnitude of zero is not always measured as being zero), by scale factors (a scale factor error is an error concerning the coefficients by which the measurement is multiplied), and by axis setting errors (orthogonality error between the measurement axes).
Document FR-A-2 824 393 discloses a method of navigation by means of an inertial unit having tied components mounted on a mechanical device that enables the unit to be placed in a succession of different positions in order to average out the errors of the gyros as projected onto the local geographical system of axes. The attitude information output by the inertial unit with tied components can be used directly for controlling the mechanical device for the purpose of placing the unit successively in different positions that are substantially stationary relative to the local geographical system of axes. More precisely, the long-term navigation method is implemented by means of an inertial unit that is associated with a tied system of axes X, Y, Z mounted on a carrier in order to measure therefrom movements relative to a geographical system of axes having fixed directions along three axes Xg, Yg, Zg, and comprising:                measurement actions consisting in using the inertial unit to permanently measure an orientation of the tied system of axes in the geographical system of axes; and        positioning actions consisting in applying a sequence of cycles of turning the inertial unit over eight times, each turnover maintaining the axis Y in a direction parallel to the axis Yg, with a succession of two turnovers about the axis X being preceded and followed by a turnover about the axis Z, and with a succession of two turnovers about the axis Z being preceded and followed by a turnover about the axis X.        
The positioning actions serve to compensate measurement errors by sign reversal along the axis Y on each turnover, by sign reversal along the axis X on each turnover about the axis Z, and by sign reversal along the axis Z at each turnover about the axis X. The measurement actions that are performed permanently then enable the errors on each of the axes X, Y, and Z of the tied system of axes to compensate mutually so as to reduce the projections of errors onto the axes Xg, Yg, and Zg by averaging their contributions over a cycle.
The method provides significant improvements in accuracy. In contrast, it is necessary to proceed with strap-down type integration of the measurements coming from the gyros. Unfortunately, such measurements include noise that, on being integrated, gives rise to navigation errors such as random walks. Those errors have an influence on the degradation of navigation performance. In addition, the measurements provided by the gyros incorporate a component associated with rotation of the Earth and thus affected by the scale factor errors specific to each gyro.
Furthermore, the method described in that document can be used only with sensors having drift error that remains constant over the entire measurement range. That method is therefore not suitable for use with vibratory gyros that are conventionally used in inertial systems used for navigation, e.g. as happens in a gyro-compass adapted to provide an angle measurement relative to a reference direction (or heading) such as geographical north. Vibratory gyros are axially symmetrical Coriolis effect gyros known as Coriolis vibratory gyros (CVG), e.g. hemispherical resonator gyros (HRG), and they are generally said to be of type I in the document “Type I and type II micromachined vibratory gyroscopes” by Andrei M. Shkel, pp. 586-593, IEEE/ION (“Institute of Electrical and Electronics Engineers/Institute of Navigation”), PLANS 2006, San Diego, Calif., USA. Those gyros operate in particular in an open loop and they enable an absolute angle of rotation to be measured on the basis of measuring an angle representing the vibration position of the gyro relative to measurement electrodes. The measurements provided by such vibratory gyros may suffer from errors that are essentially a function of the position of the vibration relative to the measurement electrode. Those errors thus vary as a function of the vibration position as represented by its electrical angle.